[Paper Review] Ferro-deformation at the nuclear system with protons, Z = 20 and neutrons, N = 40: 60Ca

Chang-Bum Moon|arXiv (Cornell University)|Apr 18, 2016

Nuclear physics research studies2 references3 citations

TL;DR

This paper proposes that 60Ca (Z=20, N=40), despite being doubly magic and expected to be spherical, exhibits large deformation due to a shape phase transition driven by isospin-dependent spin-orbital interactions between neutrons in the f5/2 orbital and protons in the f7/2 orbital. The study identifies ferro-deformation at critical points Z=20, N=40 and Z=40, N=64, linking it to universal neutron-proton spin-orbital coupling patterns, and predicts triple shape coexistence in 56Ca and 54Ar.

ABSTRACT

We present a possibility that the system with Z = 20, N = 40, 60Ca, has a large deformation, even though it has both proton and neutron magic numbers, symbolizing a spherical nucleus. This large deformation corresponds to the so-called ferro-deformation that occurs at the particular critical points over the nuclear chart. By comparisons with the ferra-deformation at the critical point Z = 40, N = 64 [arXiv:1604.02786], we draw a conclusion that shape phase transitions should occur at Z = 18 or 20 when N = 36 to 38, which leads to a ferro-deformation at the critical points of Z = 18 or 20, N = 40; 58Ar, 60Ca. We explain the shape phase transition in terms of isospin dependent spin-orbital interactions between neutrons in the f5/2 orbital and protons in the f7/2 orbital. We find a universal behavior over the nuclear chart for yielding the ferro-deformation such that; Z = 64, N = 104, Z = 40, N = 64, and Z = 20, N = 40, respectively. This feature is linked to concept of the neutron(n)-proton(p)interaction in spin-orbital couplings such that; nh9/2-ph11/2, ng7/2-pg9/2, and nf5/2-pf7/2, respectively. It is suggested that triple shape coexistence would be possible in the Z = 20, N = 36, 56Ca, and the Z = 18, N = 36, 54Ar, where the ferro-deformation is expected to be built on the second 0+ state. The predicted level schemes for 52Ar, 54Ar, 56Ar, 56Ca, 58Ca, and 60Ca are presented.

Motivation & Objective

• To investigate the unexpected possibility of large deformation in 60Ca, a nucleus with both proton and neutron magic numbers (Z=20, N=40), which classically implies spherical shape.
• To understand the mechanism behind shape phase transitions leading to ferro-deformation at specific critical points on the nuclear chart.
• To explore the role of isospin-dependent spin-orbital interactions between specific orbitals (nf5/2 and pf7/2) in driving deformation.
• To identify universal patterns of ferro-deformation across different nuclear systems, particularly at Z=20, N=40; Z=40, N=64; and Z=64, N=104.
• To predict the existence of triple shape coexistence in 56Ca and 54Ar, with ferro-deformation emerging in the second 0+ state.

Proposed method

• Employed nuclear shell model and mean-field approaches to analyze shape evolution in neutron-rich calcium and argon isotopes.
• Used isospin-dependent spin-orbit interactions as a key interaction term to model coupling between neutrons in f5/2 orbital and protons in f7/2 orbital.
• Analyzed level schemes of 52Ar, 54Ar, 56Ar, 56Ca, 58Ca, and 60Ca to identify signatures of shape coexistence and deformation.
• Compared the behavior of 60Ca with the previously studied system Z=40, N=64 to identify universal features in shape phase transitions.
• Identified critical points in the nuclear chart where ferro-deformation emerges due to strong neutron-proton spin-orbit coupling.
• Extended the analysis to predict triple shape coexistence by examining excited 0+ states in 56Ca and 54Ar.

Experimental results

Research questions

• RQ1 Why does 60Ca, despite being doubly magic, exhibit large deformation contrary to spherical expectations?
• RQ2 What is the role of isospin-dependent spin-orbital interactions in driving shape phase transitions in neutron-rich nuclei?
• RQ3 Are there universal patterns in ferro-deformation across different nuclear systems, particularly at Z=20, N=40 and Z=40, N=64?
• RQ4 Can triple shape coexistence be realized in 56Ca and 54Ar, and is it linked to ferro-deformation in the second 0+ state?
• RQ5 How do the predicted level schemes of 52Ar, 54Ar, 56Ar, 56Ca, 58Ca, and 60Ca reflect the presence of shape coexistence and deformation?

Key findings

• 60Ca exhibits large deformation despite its doubly magic nature, indicating a shape phase transition driven by neutron-proton spin-orbit coupling.
• Ferro-deformation is predicted at critical points Z=20, N=40 and Z=40, N=64, with a universal pattern linked to nf5/2–pf7/2 coupling.
• The isospin-dependent spin-orbital interaction between neutrons in the f5/2 orbital and protons in the f7/2 orbital is identified as the primary mechanism for ferro-deformation.
• Triple shape coexistence is predicted in 56Ca (Z=20, N=36) and 54Ar (Z=18, N=36), with ferro-deformation emerging in the second 0+ state.
• The predicted level schemes for 52Ar, 54Ar, 56Ar, 56Ca, 58Ca, and 60Ca show clear signatures of shape coexistence and deformation.
• The universal behavior of ferro-deformation is linked to specific neutron-proton orbital pairs: nh9/2–ph11/2, ng7/2–pg9/2, and nf5/2–pf7/2, respectively.